Slower rendering when using paths - winforms

Question

Why does the following code render much more slowly when using a path as opposed to drawing each line individually?
If I draw each line individually, window resizing seems ok, but if I use a path, the resizing is very laggy.
public class GdiRenderCanvas : System.Windows.Forms.Control
{
System.Drawing.Drawing2D.GraphicsPath path = null;
public GdiRenderCanvas()
{
SetStyle(System.Windows.Forms.ControlStyles.AllPaintingInWmPaint | System.Windows.Forms.ControlStyles.UserPaint, true);
DoubleBuffered = true;
ResizeRedraw = true;
path = new System.Drawing.Drawing2D.GraphicsPath();
Random r = new Random(8);
for (int i = 0; i < 1000; ++i)
{
int x = (int)(r.NextDouble() * 800);
int y = (int)(r.NextDouble() * 800);
int x1 = (int)(r.NextDouble() * 800);
int y1 = (int)(r.NextDouble() * 800);
path.AddLine(x, y, x1, y1);
path.CloseFigure();
}
}
protected override void OnPaint(System.Windows.Forms.PaintEventArgs e)
{
e.Graphics.SmoothingMode = System.Drawing.Drawing2D.SmoothingMode.AntiAlias;
e.Graphics.InterpolationMode = System.Drawing.Drawing2D.InterpolationMode.Bilinear;
if (false)
{
Random r = new Random(8);
for (int i = 0; i < 1000; ++i)
{
int x = (int)(r.NextDouble() * 800);
int y = (int)(r.NextDouble() * 800);
int x1 = (int)(r.NextDouble() * 800);
int y1 = (int)(r.NextDouble() * 800);
e.Graphics.DrawLine(pen, x, y, x1, y1);
}
}
else
{
e.Graphics.DrawPath(pen, path);
}
}
System.Drawing.Pen pen = new System.Drawing.Pen(System.Drawing.Color.Red, 1);
}